Considering the anisotropy of the earth media is helpful in reducing the depth error between seismic and drilling and providing reliable imaging data for seismic interpretation and inversion. Transversely isotropic media with a vertical axis of symmetry are the most common type of anisotropic media and have been under constant study. The separation of the P‐ and S‐wavefields, which affects the accuracy of elastic wave imaging and the inversion in transversely isotropic media with a vertical axis of symmetry, is a hot research topic. Among the commonly used wavefield decoupling methods, the S‐wave is typically obtained by subtracting the P‐wave from the total wavefield. However, this kind of wavefield decoupling method often leads to severe P‐wave crosstalk in the separated S‐wavefield; thus, it needs further development. In this paper, the principle that the divergence of the S‐wave is zero is employed to solve the unresolved S‐wave elastic parameters of the S‐wave stiffness matrix by utilizing the modified zero‐order pseudo‐Helmholtz decomposition operator. The obtained S‐wave elastic parameters are employed to construct the qS‐wave stress and facilitate the derivation of the relationship between the qS‐wave particle velocity and the qS‐wave stress. Furthermore, a qS‐wave decoupling first‐order velocity–stress equation, which matches the qP‐wave decoupling first‐order velocity–stress equation, is derived. By jointly using the decoupling equations of qS‐ and qP‐wave, the separation of the P‐ and S‐wavefields in transversely isotropic media with a vertical axis of symmetry is realized. The efficiency of the proposed method is demonstrated via numerical tests conducted to assess the wavefield separation. Moreover, a complex model is employed to perform elastic reverse‐time migration, resulting in the acquisition of accurate imaging results for PP, PS, SP, and SS waves, without the presence of significant artefacts. The correctness of the qS‐wave decoupling equation in transversely isotropic media with a vertical axis of symmetry is confirmed by the comparative tests using decoupling methods in isotropic media.

中文翻译：

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横观各向同性介质中波场分离的qS波解耦方程

考虑地球介质的各向异性，有助于减少地震与钻井之间的深度误差，为地震解释和反演提供可靠的成像数据。具有垂直对称轴的横向各向同性介质是最常见的各向异性介质类型，并且一直在不断研究。 P波场和S波场的分离影响弹性波成像和具有垂直对称轴的横观各向同性介质反演的精度，是一个热点研究课题。在常用的波场解耦方法中，S波通常是通过从总波场中减去P波来获得的。然而，这种波场解耦方法往往会导致分离的S波场中存在​​严重的P波串扰；因此，它需要进一步发展。本文利用横波发散度为零的原理，利用修正的零阶伪亥姆霍兹分解算子求解横波刚度矩阵中未解的横波弹性参数。利用获得的横波弹性参数来构造qS波应力，并有利于推导qS波质点速度与qS波应力之间的关系。此外，还推导了与qP波解耦一阶速度-应力方程相匹配的qS波解耦一阶速度-应力方程。通过联合使用qS波和qP波的解耦方程，实现了具有垂直对称轴的横观各向同性介质中P波场和S波场的分离。通过评估波场分离的数值测试证明了所提出方法的效率。此外，采用复杂模型进行弹性逆时偏移，从而获得 PP、PS、SP 和 SS 波的精确成像结果，且不存在明显的伪影。通过各向同性介质中解耦方法的对比试验，证实了具有垂直对称轴的横观各向同性介质中qS波解耦方程的正确性。